have you met the standard theorem I allude to? it can be shown without appeal to it as well, and you should probably do that. HINT

1 = 1-P+P

where 1 means the identity matrix.

have you done the computation to show 1-P is a projection? (recall a projection is a map Q such that Q^2=Q, or equally, Q(1-Q)=0. what is the characteristic polynomial of Q? what is the minimal poly of Q if Q is neither 1 nor the zero map?)

if you can't see how to start a question it is always advisable to read the notes that tell you the defining properties of what you wish to demonstrate.